One special geometric property of an eight-by-eight chessboard is that no single square can be considered the absolute center of it. This somewhat trivial fact opens up some intriguing possibilities when it comes to seemingly symmetrical positions. When the axis of symmetry is a file, the curious case of the spare a-file (and the phantom i-file) can occur.
[caption id="attachment_165073" align="alignnone" width="300"]
White to play and mate in six moves - T.R. Dawson (1920)[/caption]
When the white knight moves, the black king can only travel back and forth between e4-f5/d5. If white can bring the knight to e8 at the opportune time, Nd6# or Nf6# will follow.
It’s easy enough to get the knight to e8 in five moves via the scenic e3-c2-b4-a6-c7-e8 route. 1.Nc2 Kd5 (or Kf5) 2.Nb4+ Ke4 3.Na6 Kd5 4.Nc7+ Ke4 5.Ne8 Kd5 6.Nf6#.
More than the solution, what interests us is the fact that despite the seemingly symmetrical placement of pieces around the e-file axis, there is only one correct solution. The knight just can’t reach the e8 square by taking the mirrored e3-g2-h4 route.
That spare file on one wing makes all the difference in the following problem as well.
[caption id="attachment_165074" align="alignnone" width="300"]
White to play and mate in two moves[/caption]
It is clear that white must threaten a checkmate with the queen. Black must move one of the pawns next move, so a move like Qh1 (Qh5# if the f-pawn moves ; Qc6# if the d-pawn moves) feels natural, but black can thwart this plan with 1...d5. Similarly 1.Qb1 runs into 1...f5.
Then the solution has to be something like 1.Qh4. Now irrespective of which black pawn moves forward, white mates with either 2.Qh5# or 2.Qa4#. Shouldn’t 1.Qb4 - the mirror image move - work too? It turns out that after 1...f6 (or 1...f5), white needs to play the impossible 2.Qi4# in that case.
Here’s another, albeit slightly difficult, problem of the same ilk.
[caption id="attachment_165075" align="alignnone" width="300"]
White to play and mate in two moves - George E. Carpenter (1873)[/caption]
White can move the queen and let black take one of the knights. There are two beautiful mirror mates ; 1...Kxf5 2.Qg6# and 1...Kxd5 Qc6#. But tries like 1.Qg6 or 1.Qb6 do not work because the black king can also go to d3 or f3.
Once again, the spare a-file is key. 1.Qa6 Kf3 2.Qe2#.
All these pretty problems are composed ones. That makes one think, is there any practical value in knowing about the existence of this spare file? Indeed, there is.
Here’s a very practical endgame training position.
[caption id="attachment_165076" align="alignnone" width="300"]
White to play - Assess the position[/caption]
White must play either 1.c4 or 1.g4 and trigger a pawn promotion race. Does it make a difference which pawn you move first? In both lines white just about wins the pawn race, but is it enough to win?
Both options (1.c4 Kf6 2.Kd5 Kf5 3.Kxc5 Kg4 4.Kd4 Kxg3 5.c5 g4 6.c6 Kf2 7.c7 g3 8.c8=Q g2 and 1.g4 Kd6 2.Kf5 Kd5 3.Kxg5 Kc4 4.Kf4 Kxc3 5.g5 Kb2 6.g6 c4 7.g7 c3 8.g8=Q c2 ) lead to similar “Queen versus 7th rank pawn” situations. Does the spare a-file make a difference? Indeed, it does.
Let’s consider the line starting with 1.g4. It ends up with a position like this.
[caption id="attachment_165077" align="alignnone" width="300"]
After 8...c2[/caption]
In such situations, the defender can earn a draw only in certain cases. This happens to be one of them. This great escape is only possible because in certain situations black can play Ka1 (as opposed to Kc1) when the white queen can’t capture the pawn on c2 due to stalemate.
In the other line starting with 1.c4, black gets saddled with the g-pawn and loses. Why? Because the black king can’t seek refuge in that all important phantom ‘i-file’.
White to play and mate in six moves - T.R. Dawson (1920)[/caption]
When the white knight moves, the black king can only travel back and forth between e4-f5/d5. If white can bring the knight to e8 at the opportune time, Nd6# or Nf6# will follow.
It’s easy enough to get the knight to e8 in five moves via the scenic e3-c2-b4-a6-c7-e8 route. 1.Nc2 Kd5 (or Kf5) 2.Nb4+ Ke4 3.Na6 Kd5 4.Nc7+ Ke4 5.Ne8 Kd5 6.Nf6#.
More than the solution, what interests us is the fact that despite the seemingly symmetrical placement of pieces around the e-file axis, there is only one correct solution. The knight just can’t reach the e8 square by taking the mirrored e3-g2-h4 route.
That spare file on one wing makes all the difference in the following problem as well.
[caption id="attachment_165074" align="alignnone" width="300"] White to play and mate in two moves[/caption]
It is clear that white must threaten a checkmate with the queen. Black must move one of the pawns next move, so a move like Qh1 (Qh5# if the f-pawn moves ; Qc6# if the d-pawn moves) feels natural, but black can thwart this plan with 1...d5. Similarly 1.Qb1 runs into 1...f5.
Then the solution has to be something like 1.Qh4. Now irrespective of which black pawn moves forward, white mates with either 2.Qh5# or 2.Qa4#. Shouldn’t 1.Qb4 - the mirror image move - work too? It turns out that after 1...f6 (or 1...f5), white needs to play the impossible 2.Qi4# in that case.
Here’s another, albeit slightly difficult, problem of the same ilk.
[caption id="attachment_165075" align="alignnone" width="300"] White to play and mate in two moves - George E. Carpenter (1873)[/caption]
White can move the queen and let black take one of the knights. There are two beautiful mirror mates ; 1...Kxf5 2.Qg6# and 1...Kxd5 Qc6#. But tries like 1.Qg6 or 1.Qb6 do not work because the black king can also go to d3 or f3.
Once again, the spare a-file is key. 1.Qa6 Kf3 2.Qe2#.
All these pretty problems are composed ones. That makes one think, is there any practical value in knowing about the existence of this spare file? Indeed, there is.
Here’s a very practical endgame training position.
[caption id="attachment_165076" align="alignnone" width="300"] White to play - Assess the position[/caption]
White must play either 1.c4 or 1.g4 and trigger a pawn promotion race. Does it make a difference which pawn you move first? In both lines white just about wins the pawn race, but is it enough to win?
Both options (1.c4 Kf6 2.Kd5 Kf5 3.Kxc5 Kg4 4.Kd4 Kxg3 5.c5 g4 6.c6 Kf2 7.c7 g3 8.c8=Q g2 and 1.g4 Kd6 2.Kf5 Kd5 3.Kxg5 Kc4 4.Kf4 Kxc3 5.g5 Kb2 6.g6 c4 7.g7 c3 8.g8=Q c2 ) lead to similar “Queen versus 7th rank pawn” situations. Does the spare a-file make a difference? Indeed, it does.
Let’s consider the line starting with 1.g4. It ends up with a position like this.
[caption id="attachment_165077" align="alignnone" width="300"] After 8...c2[/caption]
In such situations, the defender can earn a draw only in certain cases. This happens to be one of them. This great escape is only possible because in certain situations black can play Ka1 (as opposed to Kc1) when the white queen can’t capture the pawn on c2 due to stalemate.
In the other line starting with 1.c4, black gets saddled with the g-pawn and loses. Why? Because the black king can’t seek refuge in that all important phantom ‘i-file’.